Chapter 



CHANGE 



2/1. The most fundamental concept in cybernetics is that of 

 "difference", either that two things are recognisably different or that 

 one thing has changed with time. Its range of application need not 

 be described now, for the subsequent chapters will illustrate the 

 range abundantly. All the changes that may occur with time are 

 naturally included, for when plants grow and planets age and 

 machines move some change from one state to another is implicit. 

 So our first task will be to develop this concept of "change", not 

 only making it more precise but making it richer, converting it to a 

 form that experience has shown to be necessary if significant develop- 

 ments are to be made. 



Often a change occurs continuously, that is, by infinitesimal steps, 

 as when the earth moves through space, or a sunbather's skin 

 darkens under exposure. The consideration of steps that are 

 infinitesimal, however, raises a number of purely mathematical 

 difficulties, so we shall avoid their consideration entirely. Instead, 

 we shall assume in all cases that the changes occur by finite steps in 

 time and that any difference is also finite. We shall assume that the 

 change occurs by a measurable jump, as the money in a bank account 

 changes by at least a penny. Though this supposition may seem 

 artificial in a world in which continuity is common, it has great 

 advantages in an Introduction and is not as artificial as it seems. 

 When the differences are finite, all the important questions, as we 

 shall see later, can be decided by simple counting, so that it is easy to 

 be quite sure whether we are right or not. Were we to consider 

 continuous changes we would often have to compare infinitesimal 

 against infinitesimal, or to consider what we would have after adding 

 together an infinite number of infinitesimals — questions by nc 

 means easy to answer. 



As a simple trick, the discrete can often be carried over into the 

 continuous, in a way suitable for practical purposes, by making a 

 graph of the discrete, with the values shown as separate points. It is 



9 



